A note on limiting distribution of the sample auto-covariance function for the first-order autoregressive (AR(1)) model

Abstract

Auto-covariance plays a fundamental role in the theory and practice of time series in both spectral and time domain analysis. Many datasets in econometrics, finance or telecommunications follow AR(1) model. In this work, the estimation of the auto-covariance of AR(1) processes is considered. We deal with the limiting distribution of sample auto-covariance function and find its$\mathrm{ }{L}^2$-convergence distribution. The limiting result is investigated through extensive Monte Carlo simulations.

Keywords:

• AR(1)
• auto-covariance function
• limiting distribution